She knew at that point that (a) getting shot and dying makes you come back as a walker, (b) walkers don't listen to reason/verbal commands, and (c) getting bit presumably means you'll come back as a walker.
Even if she was still distracted by the fact that Artie was a good friend, the fact that she still tried to talk to the clearly-snarling guy in front of her is idiotic. She should know better, and is basically skating by right now on plot armor. That's twice in two episodes that she's nearly been bit.
I mean, it's still early yet. She, along with everyone else, is still slowly piecing everything together. I think people are still forgetting that the characters in the show don't have as much information as they do.
The first zombie she saw was the one on the news, right? A guy who was "dead" on a stretcher "came back" and started attacking/biting a guy. The two or three bullets they put into his chest didn't bring him down until one was delivered to his head. These behaviors could easily be attributed to a drug like bath salts, and that would surely be the logical conclusion someone would come to in a universe where the concept of zombies doesn't exist.
The second encounter was in a dark tunnel - plus she didn't see the body and the only person who witnessed his "death" was her drug addled son - and it was a very brief and confusing one where an injured friend of her son tried to bite her before being almost immediately run over by said son (and witnessing your son repeatedly run over his violent, yet injured, friend is a traumatic event in and of itself). She had 5 seconds to try to talk to him before he got violent and then run over.
She had no reason to believe that Artie would be affected by the sickness in the same way (and indeed, her daughter's boyfriend Matt was clearly infected and yet was still able to talk and listen to reason) so it made sense that she would try to talk to him.
And I don't think she saw any evidence that getting bitten would turn you (I mean, why
would a bite from another person kill you and then bring you back to life as a mindless flesh eater? It really makes no sense at all). All she saw in relation to that was when Matt revealed the bite mark on his neck, but the sickness had been reported all over the city and, as far as I remember, no one ever said anything about bites so in her mind the two things were unrelated.
I think her actions really do make sense in the context of her situation.
Approximately how many hours from now would the episode normally air?